text:
\section{Introduction}

\IEEEPARstart{U}{nlocking} the flexibility distributed throughout the different levels of the electricity system appears to be a decisive step for a successful energy transition. The development of demand-side management programs, the integration of Distributed Energy Resources (DERs) and the deployment of smart grid technologies give new possibilities for the system, provided that the right incentives are put in place \cite{Klonari2016, Toubeau2015}.

However, the large-scale adoption of such programs and technologies suffers the lack of a clear and coherent economic framework that will engage prosumers in a joint endeavour. The concept of consumer-centric systems aims at placing the end-users inside the economic cycle by enhancing their experience. Several visions concur for its application in power systems, each requiring different structures for the power exchanges \cite{Parag2016,Pinson2017}. In its most centralized form, it aims at extending the accessibility of the existing pool-based markets to all the prosumers and integrate them with the upstream actors \cite{Elia2018}. The efforts focus mainly on giving access to market-based signals to downstream participants, allowing price-responsive actors to optimize their bill and monetize their flexibility. This system, hence, requires enormous coordination efforts, which may necessitate significant bidirectional communication and may have privacy implications. Conversely, the most decentralized approach considers a peer-to-peer (P2P) market solution, in which consumers and producers can directly sell and buy electricity as well as related services without centralized supervision \cite{Sousa2019, Morstyn2019a,Kang2017}. In this way, they can choose how they source their electric energy, hence turning it into a product with a high potential of differentiation \cite{Morstyn2018b,Sorin2019}. By coordinating P2P transactions, Morstyn et al. \cite{Morstyn2018a} argue that it is also possible to address higher-level needs such as balancing services. However, this decentralized design relies on the complex task of properly incentivizing coordination (towards improved network efficiency) between end-users, each with different economic resources and motivations, potentially characterized by a non-rational behavior. The problem is further complicated by the inherent disparities in terms of network infrastructure. For instance, the P2P transactions fees proposed in \cite{Morstyn2020} and based on Distribution locational marginal prices discriminate prosumers based on their location on the grid. An intermediate and more practical solution consists thus in forming communities. The latter are structured around a collective of prosumers that share common interests and goals \cite{Sousa2019}, which result from a mix of subjective considerations (e.g. maximum autonomy) and/or more objective reasons (e.g. geographical proximity). Most of the current literature considers the implementation of local markets supervised by a community manager \cite{Moret2018, Cai2017}, who is responsible of both the auctions inside the local market and the power exchanges outside the community.

Overall, acting at community level offers a good compromise between centralized and fully distributed approaches. However, introducing markets in such small entities is subject to some caveats since the main assumptions of perfect competition are hardly met. For instance, the limited size of community-based markets tends to inherently give market power to some individuals.
Besides, modeling assets utility at such levels assumes that the demand is elastic, whereas it is hard to conceive that residential prosumers or small businesses would significantly modify their energy needs on a daily basis.

In order to avoid issues related to market-based transactions, an alternative approach to enable consumer-centricity is to build communities in which cooperation prevails over competition. Such a solution consists in sharing the aggregated flexibility in a fair and optimal manner based on objective costs, needs and constraints, and can be perceived as a concept enhancing costs-awareness and virtuous interactions.
Various contributions address these considerations in scenarios involving groups of interacting members \cite{Mohsenian-Rad2010a,Hupez2018,Atzeni2012,Baharlouei2013,Stevanoni2019,Lee2014,Han2019}. Among them, game theoretical approaches are commonly used when strategic behaviors are possible. On the one hand, non-cooperative games are formulated when interactions are not subject to binding agreements \cite{Mohsenian-Rad2010a,Hupez2018,Atzeni2012,Baharlouei2013, Stevanoni2019}. By designing the game appropriately, it is possible to make cooperation self-enforcing through its Nash equilibrium. In \cite{Mohsenian-Rad2010a}, an aggregative game solving the day-ahead energy consumption scheduling for a set of users owning time flexible appliances is formulated. The problem is solved using an autonomous and distributed best response algorithm, and it is shown that the outcome is equivalent to the one of the global optimization. The approach is complemented in \cite{Hupez2018} by considering a liberalized framework with multiple suppliers and a Distribution System Operator (DSO) who manages grid-related aspects. These formulations, however, lack the possibility of incentivizing participants to consent higher flexibility. The introduction of DERs combined with the use of an hourly distribution of the costs in \cite{Atzeni2012} address this issue. The Nash equilibrium is computed using a proximal decomposition algorithm, but higher flexibility is obtained at the cost of a non-optimal global solution \cite{Baharlouei2013}. On the other hand, cooperative game theory focuses on incentivizing the formation of coalitions \cite{Lee2014,Han2019}. In such schemes, cooperation is based on a predefined consensus enforced by a supervizing authority. In \cite{Lee2014}, end-users form coalitions for trading a portion of their electricity. Their participation is optimized by relying on the Shapley value for adequately distributing energy savings. Han et al. \cite{Han2019} propose a similar approach, which is complemented with an energy management optimization.
Such a predefined consensus allows to explicitly define how costs are distributed among end-users, thus ensuring fairness within the community. However, two shortcomings still need to be addressed in the current literature.
Firstly, current works focus on commodity costs, and neglect network-related fees, while the latter contribution represents the highest expenditures within the electricity bill. Secondly, they fail to consider that the local generation and flexibility can be valued at another price than the utility costs within the community (e.g. the truth marginal cost of photovoltaic generation is near zero), which may limit the mutualization potential of the available resources.

In this context, this paper proposes an original day-ahead cooperative framework aiming to minimize both commodity and network costs in a low voltage entity, without resorting to a complex market structure. A fair distribution of the cost savings is targeted to leverage the involvement of all its members and enhance the sharing of DERs. Practically, we compare two different distribution keys, namely a natural consensus arising from the Nash equilibrium, and a solution provided by the Shapley value.
The proposed framework fits naturally to a distributed resolution such as the Alternating Direction Method of Multipliers \cite{Boyd2010}, hence ensuring that no third-party is necessary for the reliable operation of the proposed design. The transparent computation and supervision (required to guarantee the safety and effectiveness of the proposed design) could be given by a blockchain and smart contracts \cite{Munsing2017}, such that the proposed concept naturally conforms within the current liberalized framework. Overall, the main contributions of this paper are the following:

\begin{itemize}
\item We establish a community framework where DERs and flexible resources are naturally mutualized by recording virtual power flows. The excess of generation and storage pertaining to individual end-users is thus made available to the rest of the community. This solution complies with the current liberalized context and raises engagement opportunities at the local level, thereby improving the cost-effectiveness of traditional strategies where each individual only considers its own electricity.
\item We formulate a day-ahead power exchange planning that minimizes the global community costs. The procedure accounts for grid fees and losses through the Second Order Cone Programming (SOCP) relaxation of power flow equations (DistFlow). This also allows for the enforcement of a scheduling solution that complies with the network's technical requirements. Furthermore, by considering the non-linear and aggregative nature of the grid costs, we acknowledge that the grid is a shared asset whose operation can be optimized through cooperation within the community.
\item We apply two different cost distributions to ensure the fairness in the final electricity bill of end-users. The goal is to allocate among individuals the costs savings from the mutualized flexibility in a transparent and rational manner. In particular, outcomes from the case study show that the consensus given by the Nash equilibrium tends to value the potential flexibility consented by end-users, while the Shapley value better rewards the actual mobilized flexibility.
\end{itemize}
This combination of a cost structure reflecting more accurately the use of resources with a framework enhancing higher engagement potential and a fair cost allocation to ensure the achievement of the scheme gives a holistic and innovative solution to help fulfill the energy transition objectives on the demand-side. The rest of the paper is structured as follows. Section \ref{sec:community} lays out the proposed community framework. In particular, the load, network and cost models are successively introduced. The mechanisms of the proposed design, i.e. the optimization problem and the cost distributions, are presented in Section \ref{sec:PES}. Finally, Section \ref{sec:case_studies} presents a case study and highlights interesting observations, before the conclusions and perspectives are drawn in Section \ref{sub:Conclusion}.

\section{Community framework}
\label{sec:community}
In order to adopt a scenario in which network considerations are fully integrated, it is assumed that community members are connected to the same low voltage (LV) entity (such as a distribution feeder or a collection of them). The proposed design can be seamlessly integrated into the current liberalized framework: the community network is managed by a single DSO, while each member can choose among different suppliers for its net consumption $l_{n}^{t}$ (accounting for the mutualization of resources with other end-users). Besides, note that curly inequality operators (e.g. $\succeq$) are used for component-wise inequalities and the delta-equal-to symbols ($\triangleq$) define variables or sets.

Let $n \in \mathcal{N}\triangleq\{1,2,\ldots,N\}$ denote the set of community members, and $t \in \mathcal{T} \triangleq\{1,\ldots,T\}$ the set of optimization intervals considered for one day of scheduling, each of duration $\Delta t$. To enable more efficient power exchanges through mutualization of all individual resources, the electricity flows are differentiated between virtual and physical flows (Fig.~\ref{fig:community_bill}). Virtual flows $l_{n}^{t}$ record the energy transactions of the prosumers for billing purposes, and do not necessarily reflect the actual physical flows within the network. Obviously, the sum of all virtual and physical flows are equal.

\begin{figure}[!b]
\centering
\includegraphics[scale=0.36]{Figure1.eps}
\caption{Community bill formation based on virtual and physical flows.}
\label{fig:community_bill}
\end{figure}

\subsection{Prosumer load model}
For each community member $n\in\mathcal{N}$, we can distinguish different load components. We firstly define the flexible consumption, i.e. the portion of the load for which prosumers consent flexibility in their operation (e.g. washing machine, heat pump, electric vehicle, etc.). This set of appliances, denoted by $\mathcal{A}_n$, can be operated at the most opportune time under intertemporal constraints (some processes have fixed load profiles and/or cannot be stopped during operation). Each appliance $a\in\mathcal{A}_n$ is described by a power scheduling vector:
\begin{equation}
\mathbf{x}_{n,a} \triangleq \left[ x_{n,a}^1 ,\ldots, x_{n,a}^T \right] \succeq 0\text{,}
\end{equation}
which is formed by the collection of the corresponding values at time intervals $t\in \mathcal{T}$.

Secondly, the non-flexible load includes critical appliances (e.g. lighting, kitchen equipment, multimedia devices, etc.) as well as the non-dispatchable local generation, that is, energy produced by photovoltaic (PV) panels and small wind turbines, counted negatively. Its forecasted power vector \cite{Toubeau2019} is defined by:
\begin{equation}
\mathbf{d}_{n} \triangleq \left[ d_{n}^1 ,\ldots, d_{n}^T \right]\text{.}
\end{equation}

Thirdly, prosumers can have a personal Energy Storage System (ESS) such as a battery. The power scheduling vector $\mathbf{s}_{n,\mathrm{ind}}$ for their own utilization is:
\begin{equation}
\mathbf{s}_{n,\mathrm{ind}} \triangleq \left[ s_{n,\mathrm{ind}}^1 ,\ldots, s_{n,\mathrm{ind}}^T \right]\text{,}
\end{equation}
where a positive value stands for the charging mode. Then, each member makes its excess storage space available to other members in need. The power hosted $\mathbf{s}_{n,\mathrm{host}}$ is defined by:
\begin{equation}
\mathbf{s}_{n,\mathrm{host}} \triangleq \left[ s_{n,\mathrm{host}}^1 ,\ldots, s_{n,\mathrm{host}}^T \right]\text{.}
\end{equation}

Therefore, the end-users can possibly benefit from the excess of storage space pooled by the other members of the community. The corresponding power scheduling vector $\mathbf{s}_{n,\mathrm{mut}}$ of shared ESS space allocated to member $n$ is:
\begin{equation}
\mathbf{s}_{n,\mathrm{mut}} \triangleq \left[ s_{n,\mathrm{mut}}^1 ,\ldots, s_{n,\mathrm{mut}}^T \right]\text{.}
\end{equation}

Similarly, the excess of power generated (i.e. outflows of end-users) within the community is made available to other members. The portion allocated to member $n$ is given by:
\begin{equation}
\mathbf{v}_{n} \triangleq \left[ v_{n}^1 ,\ldots, v_{n}^T \right] \succeq 0\text{.}
\end{equation}

Hence, the individual virtual net load (which is referred to as net load in the remainder of the paper) metered by the DSO at time step $t$ (Fig. \ref{fig:community_bill}) is defined as:
\begin{equation}
l_n^t = d_n^t + \sum_{a\in\mathcal{A}_{n}} x_{n,a}^t + s_{n,\mathrm{ind}}^t - v_n^t + s_{n,\mathrm{mut}}^t\text{.} \label{eq:netcons}
\end{equation}

Additionally, the load scheduling variables are subject to individual requirements and physical constraints. We thereby characterize the scheduling flexibility for each appliance $a$ of member $n$ by a permissibility vector:
\begin{equation}
\boldsymbol{\pi}_{n,a} \triangleq \left[\pi_{n,a}^1,\ldots,\pi_{n,a}^T\right],\qquad\pi_{n,a}^t \in \left\lbrace  0,1 \right\rbrace \text{.}
\end{equation}

This binary vector specifies the time intervals during which the member agrees for its appliance to be scheduled (1:~permitted, 0: not permitted). If the total predetermined energy consumption of appliance $a$ is $E_{n,a}$, the resulting power profile constraints are:
\begin{equation}
\boldsymbol{\pi}_{n,a} \cdot \mathbf{x}_{n,a}^{\mathbf{T}} \cdot \Delta t = E_{n,a}
\end{equation}
\begin{equation}
\mathrm{NOT}(\boldsymbol{\pi}_{n,a}) \cdot \mathbf{x}_{n,a}^{\mathbf{T}} = 0\text{.}
\end{equation}

Besides, loads are subject to power consumption constraints. Some appliances have predetermined consumption cycles (e.g. washing machine) while others have modular cycles (e.g. electric vehicles). For the sake of simplicity and without loss of generality, it is considered that flexible consumption is fully modular. Hence, each appliance is limited only by a maximum power level $M_{n,a}$:
\begin{equation}
0 \preceq \mathbf{x}_{n,a} \preceq M_{n,a}\text{.}
\end{equation}

In our simplified model, ESS are characterized by a maximum energy capacity $K_n$ as well as maximum power levels in charge $M_{n}^{\mathrm{ch}}$ and discharge $M_{n}^{\mathrm{dis}}$ modes:
\begin{IEEEeqnarray}{c}
0\preceq \mathbf{e}_{n,\mathrm{ind}} + \mathbf{e}_{n,\mathrm{host}} \preceq K_n  \\
-M_{n}^{\mathrm{dis}} \preceq \mathbf{s}_{n,\mathrm{ind}} + \mathbf{s}_{n,\mathrm{host}} \preceq M_{n}^{\mathrm{ch}}\text{,}
\end{IEEEeqnarray}
where $\mathbf{e}_{n,\mathrm{ind}} \triangleq \left[ e_{n,\mathrm{ind}}^1 ,\ldots, e_{n,\mathrm{ind}}^T \right]$ is the available stored energy for personal use and $\mathbf{e}_{n,\mathrm{host}} \triangleq \left[ e_{n,\mathrm{host}}^1 ,\ldots, e_{n,\mathrm{host}}^T \right]$ the available stored energy on behalf of other members, whose elements are respectively obtained by:
\begin{IEEEeqnarray}{c}
e_{n,\mathrm{ind}}^t = e_{n,\mathrm{ind}}^{t-1} + \Delta t \cdot s_{n,\mathrm{ind}}^t; \quad e_{n,\mathrm{ind}}^t \geq0 \quad \forall t \in \mathcal{T} \\
e_{n,\mathrm{host}}^t = e_{n,\mathrm{host}}^{t-1} + \Delta t \cdot s_{n,\mathrm{host}}^t; \quad e_{n,\mathrm{host}}^t \geq0 \quad \forall t \in \mathcal{T}\text{.} \quad
\end{IEEEeqnarray}
The sum of the two vectors, $\mathbf{e}_{n,\mathrm{ind}}+\mathbf{e}_{n,\mathrm{host}}=\mathbf{e}_{n,\mathrm{tot}}$, hence defines the actual ESS state of charge. Additionally, the sum of charging power vectors attributed from the pool of excess storage space to each member, $s_{n,\mathrm{mut}}$, must equal the sum of the hosting charges in the batteries $s_{n,\mathrm{host}}$, that is:
\begin{equation}
    \sum_{n \in\mathcal{N}}\mathbf{s}_{n,\mathrm{mut}} = \sum_{n \in\mathcal{N}}\mathbf{s}_{n,\mathrm{host}}\text{.}
\end{equation}
Indeed, whereas the first sum represents a pool of virtual storage power in the eyes of the members in need, the second traces the actual physical flows of the contributing members in excess.
Note that the attributed shared ESS energy $\mathbf{e}_{n,\mathrm{mut}} \triangleq \left[ e_{n,\mathrm{mut}}^1 ,\ldots, e_{n,\mathrm{mut}}^T \right]$ is obtained by:
\begin{equation}\label{eq_e_mut2}
e_{n,\mathrm{mut}}^t = e_{n,\mathrm{mut}}^{t-1} + \Delta t \cdot s_{n,\mathrm{mut}}^t; \quad e_{n,\mathrm{mut}}^t \geq 0 \quad \forall t \in \mathcal{T}\text{.}
\end{equation}

\begin{figure}[!t]
\centering
\includegraphics[scale=0.36]{Figure2.eps}
\caption{Summary example of the variables involved in excess resources mutualization.}
\label{fig:battery}
\end{figure}

Similarly, constraint \eqref{eq_v_mut} limits the available shared power to the total outflows of the members (negative net flows):
\begin{equation}\label{eq_v_mut}
    \sum_{n \in \mathcal{N}} v_n^t \preceq \sum_{n \in \mathcal{N}} l_n^{t-}, \qquad \forall t \in \mathcal{T}\text{,}
\end{equation}
where $l_n^{t-} = \mathrm{max}(-l_n^t,0)$ is the negative part of $l_n^t$.

Finally, the excess of generated power is available only for the members who have a positive net load, i.e.:
\begin{equation}
v_n^t \cdot l_n^{t-} = 0, \qquad \forall t \in \mathcal{T}\text{.}
\end{equation}

\textit{Summary example to highlight the practical interest of considering virtual energy exchanges}:
Let's consider a LV feeder connecting different end-users, among which member $n$ owns both a battery and a PV system (c.f. Fig. \ref{fig:battery}). It is assumed that its production exceeds its consumption. At a given time step (typically, after mid-afternoon), it may happen that the local production exceeds the consumption, while the storage space $e_{n, \mathrm{ind}}$ is full (from the energy absorbed in previous hours). In traditional market designs, the energy surplus ($s_{n,\mathrm{mut}} \cdot \Delta t$) is either consumed by local loads or transmitted outside the community. However, in our proposed framework, the energy can be stored in the batteries of other members ($m$ and $l$ in this example). In turn, these consider that stored energy respectively as $e_{m,\mathrm{host}}$ and $e_{l,\mathrm{host}}$. Although they coincide to physical flows for members $m$ and $l$, they are transparent for their billing as only the virtual flows intervene as detailed in Section \ref{sub:cost_structure}. The rest of the surplus corresponds to a negative virtual net load $l_n^-$ that benefits partly to the other members ($v_m$ and $v_l$) if they have a positive virtual net load. Our framework therefore improves the value of local generation and flexibility at the community level.

\subsection{Power Network model}
In order to include the costs associated to power exchanges inside the community as well as to comply with the related physical constraints, the optimal power flow equations of the radial low voltage network are considered. In this work we adapt the DistFlow equations of \cite{Baran1989} to a Second Order Cone Programming (SOCP) formulation, which allows to relax the original non-convex power flow equations with a good compromise as it takes into account power losses while keeping a good computational tractability.
Each member $n$ of the community is associated to a node of the network. This node is connected to a set of adjacent nodes denoted by $\mathcal{Y}_n$. Let's introduce the variables $\varphi_{n,j}= \vert i_{n,j} \vert^2$, the squared branch current flowing between nodes $n$ and $j$, and $w_n = \vert v_n \vert^2$, the squared voltage magnitude at node $n$, where $i_{n,j}$ and $v_n$ are complex substitutes. The time superscripts $t$ have been omitted for the sake of clarity. Overall, the SOC equations of power flows for each time step $t$ are:
\addtocounter{equation}{1}
\begin{IEEEeqnarray}{ll}
p_n = \sum_{j\in \mathcal{Y}_n} p_{n,j}, &\forall n \in \mathcal{N}  \IEEEyessubnumber*\\
q_n = \sum_{j\in \mathcal{Y}_n} q_{n,j}, &\forall n \in \mathcal{N}\\
p_{n,j}^2 + q_{n,j}^2 \leq w_n \varphi_{n,j}, \qquad &\forall n,j\in \mathcal{Y}_n \label{eq:OPFc}\\
p_{n,j} + p_{j,n} = R_{n,j} \varphi_{n,j}, \qquad &\forall n,j\in \mathcal{Y}_n \\
q_{n,j} + q_{j,n} = X_{n,j} \varphi_{n,j}, \qquad &\forall n,j\in \mathcal{Y}_n \\
w_j = w_n - 2\left(R_{n,j} p_{n,j} + X_{n,j} q_{n,j} \right) \nonumber \\
\qquad + \left(R_{n,j}^2 + X_{n,j}^2\right) \varphi_{n,j}, \qquad\qquad\qquad &\forall n,j\in \mathcal{Y}_n\text{,} \qquad
\end{IEEEeqnarray}
where $p_n$ and $q_n$ are the active and reactive power injected at node $n$, $p_{n,j}$ and $q_{n,j}$ are the active and reactive branch power flowing from $n$ to $j$, while $R_{n,j}$ and $X_{n,j}$ are respectively the resistance and reactance of the branch connecting $n$ and $j$.

The equality constraint from the original Optimal Power Flow (OPF) is relaxed into an inequality constraint (\ref{eq:OPFc}), hence including the cone interior space and ensuring convexity. Both terms of the equation should tend to be equal as the objective function tends to minimize power losses (Section \ref{sec:PES}).
The link between the prosumer model and the electrical network is described by the following equation:
\begin{equation}
p_n^t = d_n^t + \sum_{a\in\mathcal{A}_{n}} x_{n,a}^t + s_{n,\mathrm{ind}}^t + s_{n,\mathrm{host}}^t\text{.}
\label{eq:physical}
\end{equation}

In contrast with (\ref{eq:netcons}), the variables $v_n^t$ and $s_{n,\mathrm{mut}}^t$ coming from the mutualization of energy surpluses are not included as they are not physically linked to the prosumer $n$. In turn, if the prosumer $n$ has available storage space, the energy from mutualized excess storage can potentially be hosted on its device, which is captured by the variable $s_{n,\mathrm{host}}^t$. The load $p_n^t$ in (\ref{eq:physical}) is referred as the physical net load on Fig. \ref{fig:community_bill}.

\subsection{Cost structure}
\label{sub:cost_structure}
The day-ahead power exchange scheduling problem is based on the minimization of the electricity costs, which consist in three contributions in the objective function:\\
\begin{enumerate}[label=\roman*)]
\item \textit{The commodity costs:} they are associated to the marginal costs of generation, and are billed by the suppliers. Each member of the community can freely choose its supplier $i\in \mathcal{S} \triangleq \{1,\ldots,n_s\}$. However, based on the consumption history and the prosumer profile, it is easy to recommend or automatically attribute the best suited supplier. It is assumed that energy is billed by suppliers according to a dynamic pricing scheme \cite{Hupez2018}. Prices are not considered to be capacity-based, i.e. they are independent of the load level, as the suppliers have a certain degree of control on their costs via their generation portfolio and market positions. This has also the advantage to provide a more legible comparison between suppliers. Besides, only the positive part of the individual net load $l_n^{t+} = \mathrm{max}(l_n^t,0)$ is billed (the negative part $l_n^{t-}$ is valorized among the community members).
Therefore, supplier $i$ applies for each of its customer $n\in \mathcal{N}_i$:
\begin{equation}
C_{\mathrm{supp},i}^t(l_n^t) =   \gamma_{\mathrm{supp},i}^t \cdot \Delta t \cdot l_n^{t+}\text{,}
\end{equation}
where $\gamma_{\mathrm{supp},i}^{t}$ is the commodity price (in \euro{}/kWh) of supplier $i$ at time $t$.
Within a cooperative community, the commodity costs associated to each individual are influenced by the internal transactions between members. To fairly monetize this mutualization of resources, it may be necessary that the final contribution of client $n$ differs from $C_{\mathrm{supp},i}^t(l_n^t)$. In that respect, two different ways to distribute the total costs $\sum_{n \in \mathcal{N}} C_{\mathrm{supp},i}^t(l_n^t)$ at the community level are presented in Section \ref{sub:cost_distribution}.
It should be noted that this costs distribution (within the community) does not affect the final revenues of the supplier $i$, i.e. $ \sum_{n\in \mathcal{N}_i} C_{\mathrm{supp},i}^t(l_n^t)$. \\
\item \textit{The upstream grid costs:} they are associated to the power flows at the interface of the community, thus reflecting the effects on transmission and upstream distribution grids. These costs $C_{\mathrm{up}}^{t} \left( p_0^t \right)$ are not proportional to the load. Hence, we consider a non-linear cost function depending on the power at the interface node $p_0^t$. Without loss of generality, we consider a quadratic cost function:
\begin{equation}
C_{\mathrm{up}}^t(p_0^t) =  \gamma_{\mathrm{up}} \cdot \left( \Delta t \cdot p_0^{t} \right)^2\text{,}
\end{equation}
where $\gamma_{\mathrm{up}}$ represents the upstream grid fees (in \euro{}/kWh$^2$). \\
\item \textit{The local grid costs:} they are directly based on the power exchanges inside the community. We assume that each member of the community is connected to the local distribution network (cf. Fig. \ref{fig:community_bill}). Two different cost items are distinguished. One is based on the power losses in the lines while the second one is based on the line power flows in order to account for the wear and tear of the assets. The cost associated to each branch, formed by a pair of nodes $(j,k) \in \mathcal{B}$, where $\mathcal{B}$ is the set of all branches of the low voltage entity, is expressed by:
\begin{IEEEeqnarray}{cl}
C_{\mathrm{loc}}^t(p_{j,k}^t) = &\Delta t \left( \gamma_{\mathrm{loss}} \left( p_{j,k}^t + p_{k,j}^t \right) \right.\nonumber \\
& \left. + \gamma_{\mathrm{flow}} \cdot \delta_{j,k} \cdot \vert p_{j,k}^t \vert \right)\text{,} \quad
\end{IEEEeqnarray}
where $\gamma_{\mathrm{loss}}$ and $\gamma_{\mathrm{flow}}$ are respectively the costs of losses and line power flows (in \euro{}/kWh), while $\delta_{j,k}$ is the distance between the two nodes $j$ and $k$.\\
\end{enumerate}

Overall, cooperating at the community level allows to positively influence all three costs contributions, i.e. through a joint consideration of (i) nodal energy exchanges (for commodity costs), and (ii)-(iii) line power flows (for grid-related fees).

\section{Power exchange scheduling}
\label{sec:PES}
\subsection{Optimization problem}
The day-ahead optimization problem minimizes the total cost of electricity consumption by the community. The benefits over a passive consumption or an individual minimization are the following:
\begin{itemize}
\item By jointly planning their consumption, end-users can find the cost-optimal trade-off between arbitrage in the dynamic pricing (i.e. shift the load when prices are low), the upstream grid costs (which are minimized by smoothing the total load over time) and the local grid costs.
\item By sharing their excess storage, they provide more flexibility to other community members, hence giving more potential to the first consideration above. Moreover, sharing excess energy from non-dispatchable sources not only provides free energy to other members but also decreases the grid costs by reducing the imports.
\item By properly coordinating storage systems and power exchanges, power flows inside the community are contained, hence decreasing the related costs.
\end{itemize}

In practice, these three benefits are deeply correlated. The objective function consists thus in jointly minimizing the following total community costs:
\begin{IEEEeqnarray}{l}
 f(\Theta)= \sum_{t=1}^T \Delta t \left[ \sum_{i \in \mathcal{S}} \left( \gamma_{\mathrm{supp},i}^t \sum_{n\in \mathcal{N}_i} l_n^{t+} \right) + \gamma_{\mathrm{up}} \cdot \Delta t \cdot \left( p_0^t \right)^2 \right. \nonumber \\
\left. + \sum_{(j,k)\in \mathcal{B}}\left( \gamma_{\mathrm{loss}} \left( p_{j,k}^t + p_{k,j}^t \right) + \gamma_{\mathrm{flow}} \left(p_{j,k}^{t+} + p_{j,k}^{t-} \right)  \delta_{j,k} \right) \right]\text{,}\quad
\label{eq:obj}
\end{IEEEeqnarray}
where $\Theta = \cup_{n\in\mathcal{N}}\Theta_n$ is the set of all decision variables including: $x_{n,a}$, $s_{n,\mathrm{ind}}$, $s_{n,\mathrm{mut}}$, $s_{n,\mathrm{host}}$ and $v_n$ for each member
$n$. The absolute active power value in (\ref{eq:obj}) is expressed using $p_{j,k}^+ = \mathrm{max}(p_{j,k},0)$ and $p_{j,k}^- = \mathrm{max}(-p_{j,k},0)$.

The day-ahead Power Exchange Scheduling (PES) problem is therefore solved by:
\begin{IEEEeqnarray}{l}
\min_{\Theta} f(\Theta) \text{ as in (\ref{eq:obj})}  \nonumber \\
\text{s.t. (7), (9)-(20)} \text{,}
\label{eq:optim}
\end{IEEEeqnarray}
which is a convex optimization problem as both the constraints and the objective function are convex. It can be solved by standard algorithms such as interior-point or subgradient methods \cite{boyd_vandenberghe_2004}. However, it can also be conveniently solved using a distributed algorithm, thereby avoiding to resort on a third-party to guarantee the safe operation of the proposed design.

\subsection{Cost distribution}
\label{sub:cost_distribution}
Computing the minimum total cost of the community may not provide sufficient leverage for committing prosumers. Their collaboration should be incentivized by an adequate cost distribution (ensuring that all individuals have a financial interest in helping the community). In this work, we investigate two different options to distribute the cost savings arising from the global optimization \eqref{eq:optim} among community members. It should be noted that introducing network fees in the definition of the cost distribution is inherently unfair as the contribution of individuals strongly depends on their geographical location and the grid infrastructure. Instead, we choose to distribute costs based on the commodity item, accounting for the consumption and sharing behaviors of the individuals. The network costs are then passed on proportionally to their net load in the second distribution scheme.

\subsubsection{Nash equilibrium}
The first possibility consists in defining a cost distribution leading to a natural consensus. To that end, we exploit the fact that is possible to define a Nash equilibrium problem while keeping the global optimum solution \cite{Hupez2018}. It has the advantage of not requiring a central authority nor any supervision.
Hence, based on \cite{Hupez2018}, the total cost is distributed according to a proportional key accounting for the optimum commodity costs they would selfishly obtain without cooperation:
\begin{equation}
b_n = \dfrac{C_{\mathrm{supp},i}^{\{n\}*}}{\sum_{m\in \mathcal{N}}C_{\mathrm{supp},i}^{\{m\}*}} C_{\mathrm{tot}}^{\{\mathcal{N}\}*}\text{,}
\label{eq:billing}
\end{equation}
where:
\begin{itemize}
    \item $C_{\mathrm{supp},i}^{\{n\}*}$ is the commodity cost of prosumer $n$, customer of supplier $i$, when it optimizes its load selfishly (without cooperation).
    \item $C_{\mathrm{tot}}^{\{\mathcal{N}\}*}$ is the solution of the optimization problem \eqref{eq:optim}.
\end{itemize}
Note that the superscripts specify the coalition involved and if the optimal value is considered ($^*$) or not. Besides, all the costs considered for billing derive from the computations across all time steps.

The billing problem \eqref{eq:billing} can also be expressed as the solution of the following Nash equilibrium problem:
\begin{itemize}
\item Players: all $N$ community members
\item Strategies: all the possible strategies of the decision variable set $\Theta_n$
\item Payoffs:
\begin{equation}
P(\Theta_n;\Theta_{-n}) = -b_n = -\dfrac{C_{\mathrm{supp},i}^{\{n\}*}}{\sum_{m\in \mathcal{N}}C_{\mathrm{supp},i}^{\{m\}*}} f(\Theta)\text{,}
\label{eq:payoff}
\end{equation}
with $\Theta_{-n} \triangleq [\Theta_1,\ldots,\Theta_{n-1},\Theta_{n+1},\ldots,\Theta_N] = \Theta\setminus\{\Theta_n\}$, the vector containing all the decision variables except those of $n$.
\end{itemize}

Given the strict convexity of (\ref{eq:payoff}), the Nash equilibrium exists and is unique \cite{Hupez2018}. Consequently, the solution can be obtained by solving (\ref{eq:billing}), which requires the computation of $N+1$ problems: $N$ selfish problems $C_{\mathrm{supp},i}^{\{n\}*}$ and the main cooperative optimization $C_{\mathrm{tot}}^{\{\mathcal{N}\}*}$.
Overall, the Nash equilibrium cannot reward participants according to their contribution in the savings. The solution tends to be more egalitarian (i.e. the costs are equally distributed among clients) and could thus be considered less incentivizing (since the offered flexibility is not properly valued at the individual level, but shared among all members). To alleviate this effect, we also study the cost distribution resulting from a derivative of the Shapley value.

\subsubsection{Shapley value}
The Shapley value is a concept of cooperative game theory assigning a share of the gains obtained by forming coalition of different actors \cite{Shapley1953}.
It allows to remunerate end-users with payoffs that correspond to their individual contributions to the gains of the community, and is characterized by a collection of desirable properties introducing a certain degree of fairness.
Let $\mathcal{Q} \subseteq \mathcal{N} $, define a coalition of size $\vert \mathcal{Q} \vert$ and the characteristic function $ v( \mathcal{S} ):2^{\mathcal{N}}\rightarrow \mathbb{R} $ describe the savings associated to the formation of $\mathcal{Q}$. A cooperation game is defined by the pair $(\mathcal{N}, v)$ and the Shapley value $\phi_n$ attributed to a given player $n$ is given by
\begin{equation}
\phi_n(v) = \sum_{\mathcal{Q} \subseteq \mathcal{N}\setminus \{n\}} \dfrac{\vert \mathcal{Q} \vert! (N - \vert \mathcal{Q} \vert - 1)!}{N!} [v(\mathcal{Q}\cup\{n\}) -v(\mathcal{Q})] \text{.}
\end{equation}

Although all the $2^N$ combinations of coalition are necessary to compute the Shapley values, it should be noted that the only coalition possible in the cost structure considered in this paper is the grand coalition, that is $\mathcal{N}$. Indeed, as previously mentioned, the network costs cannot be directly echoed to an individual or a subset of the community as the power flows depend on the joint load of all clients. Based on all the previously mentioned considerations, we propose a billing with a double distribution key. On one hand, the commodity costs are distributed according to their Shapley value (numerator of the first term in \eqref{eq:bill}) obtained on the optimum commodity cost and scaled to the actual commodity costs (remaining of the first term). On the other hand, the grid costs are allocated proportionally to the net load. The total costs $b_n$ incurred by participant $n$ are thus:
\begin{equation}
b_n = \dfrac{C_{\mathrm{supp},i}^{\{n\}*}- \phi_n(v)} {C_{\mathrm{supp}}^{\{\mathcal{N}\}*}} C_{\mathrm{supp}}^{\{\mathcal{N}\}}  + \dfrac{l_n}{\sum_{m\in \mathcal{N}}l_m} C_{\mathrm{grid}}^{\{\mathcal{N}\}}\text{,}
\label{eq:bill}
\end{equation}
where :
\begin{itemize}
\item  $C_{\mathrm{grid}}^{\{\mathcal{N}\}}$ is the sum of $C_{\mathrm{up}}^{\{\mathcal{N}\}}$ and $C_{\mathrm{loc}}^{\{\mathcal{N}\}}$, the total upstream and local grid costs.
\item $C_{\mathrm{supp}}^{\{\mathcal{N}\}*}$ is the optimum community commodity cost obtained by solving a truncated version of \eqref{eq:optim} which considers commodity costs only (i.e. excluding network costs).
\item $C_{\mathrm{supp}}^{\{\mathcal{N}\}}$ and $C_{\mathrm{grid}}^{\{\mathcal{N}\}}$ are respectively the actual commodity and grid costs of the community. They are obtained by extracting respectively the commodity and grid costs after solving the full version of \eqref{eq:optim}.
\end{itemize}
and with $C_{\mathrm{supp}}^{\{\mathcal{N}\}} + C_{\mathrm{grid}}^{\{\mathcal{N}\}}=C_{\mathrm{tot}}^{\{\mathcal{N}\}*}$, the solution of the optimization problem \eqref{eq:optim}. Note that the computation of the $2^N$ combinations of coalition costs is sufficient to calculate the bills.

\subsubsection{Benchmark}\label{section:bench}
In order to quantify the added value of both cost distributions, i.e. (i) the Nash equilibrium, and (ii) the Shapley-based payoffs, we introduce a proper benchmark that quantifies what can be achieved using individualized optimal policies (without collaboration). To that end, we consider a framework (iii) where each end-user individually minimizes its cost objective function. Practically, two different individual strategies are analyzed (in Section \ref{sec:case_studies}), which respectively account for the minimization of the commodity costs and the minimization of the grid costs over the daily scheduling horizon. Table \ref{tab:distribution} summarizes the distribution keys of the three methodologies.
\begin{table}[h!]
\centering
\caption{Distribution key summary.}
\begin{tabular}{|l|ccc|}
\hline
           & Nash (i) & Shapley (ii) & Indiv. strat. (iii) \\ \hline
$C_{\mathrm{supp}}^{\{\mathcal{N}\}}$ &\multirow{2}{*}{$\dfrac{C_{\mathrm{supp},i}^{\{n\}*}}{\sum_{m\in \mathcal{N}}C_{\mathrm{supp},i}^{\{m\}*}}$} &$\dfrac{C_{\mathrm{supp},i}^{\{n\}*}- \phi_n(v)}{C_{\mathrm{supp}}^{\{\mathcal{N}\}*}}$ & $\dfrac{C_{\mathrm{supp},i}^{\{n\}*}}{\sum_{m\in \mathcal{N}}C_{\mathrm{supp},i}^{\{m\}*}}$          \\
$C_{\mathrm{grid}}^{\{\mathcal{N}\}}$ & & $\dfrac{l_n}{\sum_{n\in \mathcal{N}}l_n}$      & $\dfrac{l_n}{\sum_{n\in \mathcal{N}}l_n}$  \\\hline
\end{tabular}
\label{tab:distribution}
\end{table}

Regarding both cooperation schemes (i)-(ii), it is necessary that participants pledge their contribution and be transparent about their engagement for the predefined consensus. This consideration could be treated by the use of a blockchain.

\section{Case studies}
\label{sec:case_studies}

\begin{figure}[!b]
\centering
\includegraphics[scale=1]{Figure3.eps}
\caption{Comparison of the total cost division for different load management scenarios.}
\label{fig:cost_approaches}
\end{figure}
\begin{figure*}[!t]
\centering
\includegraphics[scale=1]{Figure4.eps}
\caption{Temporal evolution of the personal available energy stored locally $\mathbf{e_{n,\mathrm{ind}}}$ (a), the personal available energy stored remotely $\mathbf{e_{n,\mathrm{mut}}}$ (b), the total energy stored locally $\mathbf{e_{n,\mathrm{tot}}}$ (c), the allocated portion of excess power $\mathbf{v_{n}}$ (d) and the virtual negative net load $\mathbf{l_{n}^-}$ (e) $\forall n$. Virtual (available for personal use) and physical ESS state of charge at 18h (f).}
\label{fig:scheduling}
\end{figure*}

The proposed framework is analyzed on a benchmark composed of $N$ = 3 prosumer nodes. Each of them is assigned to a load representing the equivalent of about five low voltage users, hence summing up to 15 users, so as to reflect the conditions that could be found on a residential feeder (typical Belgian feeder such as in \cite{Klonari2015}) and obtain representative power flows in the LV network. The feeder is assumed to be one kilometer long and is fully radial.
Table \ref{tab:load} summarizes the main features of the nodal loads, i.e. details about their electrical equipment, their choice of supplier (1: cheaper nights, 2: cheaper days) and their potential in terms of load flexibility. Note that in order to ease the observations, the scheduling takes place for a day comprising four time slots. Additional information regarding the LV network, the load constraints and the tariffs applied can be found in the online appendix \cite{Appendix}.
\begin{table}[h]
\centering
\caption{Summary of the end-users characteristics.}
\begin{tabular}{|l|cccc|}
\hline
       & \multicolumn{1}{l}{PV} & \multicolumn{1}{l}{ESS} & \multicolumn{1}{l}{Supplier} & \multicolumn{1}{l|}{Shiftability}  \\ \hline
Node 1 & X                      & X                       & 1                            & 28\%                                                             \\
Node 2 & X                      &                         & 1                            & 42\%                                \\
Node 3 &                        & X                       & 2                            & 56\%                               \\ \hline
\end{tabular}
\label{tab:load}
\end{table}

In what follows, we will firstly compare, in Section \ref{sec:4a}, the total costs (aggregated at the community level) between individual and cooperative approaches. Secondly, in Section~\ref{sec:4b}, we will analyze in more details how the proposed cooperative market design allows to cost-efficiently share the available flexibility among end-users, thus highlighting the interest of differentiating physical from virtual energy exchanges. Then, based on the scheduling solution obtained by the global optimization, we will investigate in Section~\ref{sec:4c} how the costs are distributed among individuals (using both the Nash equilibrium and the Shapley value). Finally, we will highlight in Section \ref{sub:comparison} the benefits of cooperation by comparing the global cooperative optimization with a traditional framework where each end-user optimizes its own electricity bill with fixed grid fees.

\subsection{Day-ahead scheduling of end-users}\label{sec:4a}
A comparison of the total costs for three different load management approaches are displayed in Fig. \ref{fig:cost_approaches}.
The first two are the individual strategies briefly presented in Section \ref{section:bench} as a benchmark to quantify the added value of the global optimization. Firstly, we consider a basic situation, referred to as Commodity-Only (CO), where each individual optimizes its own commodity costs (by using its own flexibility to shift the load during off-peak prices), thus obtaining $C_{\mathrm{supp},i}^{\{n\}*} \forall n$. The second approach applies the Peak-to-Average Ratio (PAR), where end-users try to integrate network costs in their own objective function. However, since these two policies do not involve cooperation at the community level, there is a lack of global vision that limits their potential.
This effect is quantified by solving the global optimization \eqref{eq:optim}, which yields the total commodity costs of the community $C_{\mathrm{supp}}^{\{\mathcal{N}\}}$.

Interestingly, introducing the Peak-to-Average Ratio (PAR) allows to decrease the total costs in comparison with the individual minimization of commodity costs (Fig. \ref{fig:cost_approaches}). Indeed, by exclusively focusing on commodity costs, end-users tend to concentrate their energy consumption at specific time slots (when dynamic prices are the lowest). This behavior results in consumption peaks that significantly increase the grid costs. This effect is further exacerbated when all clients rely on the same incentives (i.e. when they have similar commodity tariff schemes). The PAR optimization alleviates this issue through a better homogenization of the energy exchanges along the day, hence leading to higher commodity costs but to a significant reduction of both grid fees components (within and outside the community).
Overall, it is important to emphasize that these two individual approaches probably represent optimistic individual behaviors as they assume that each individual will optimize its flexible resources on a daily basis. A more passive behavior of end-users or a lack of control means would surely yield higher costs.
These optimistic outcomes from both individual optimization are nonetheless outperformed by the global optimization \eqref{eq:optim}, since the latter takes advantage of the flexibility of all available resources. The cooperative framework achieves the minimal costs for the three contributions of the final electricity bill. This arises from the inclusion of energy sharing mechanisms that enable to optimally share inter-participant flexibility, i.e. excess mutualized storage space and photovoltaic generation. As the billing of each individual is based on the total cost, decreasing net imports of other individuals through the provided flexibility benefits the whole community.

\subsection{Benefits of the community-based optimization}
\label{sec:4b}
If we focus on the solution of the global optimization, the relevance of the different energy sharing mechanisms can be easily highlighted. For instance, node 1, whose end-users present a poor load shiftability (c.f. Table \ref{tab:load}), could not leverage its DERs (excess production and storage), available mostly in the afternoon, without sharing. Indeed, most of its load must be planned in the night and morning. In contrast, we observe that when the global optimization is considered, node 1 hosts a significant amount of energy for node 3 and a small quantity for node 2. Indeed, from (a-c) on Fig. \ref{fig:scheduling}, it can be identified that most of the energy stored at node 1 is not for personal use ($e_{1,\mathrm{tot}}^{18h} \gg e_{1,\mathrm{ind}}^{18h}$) and that $e_{2,\mathrm{mut}}^{18h}$ and $e_{3,\mathrm{mut}}^{18h}$ are both positive. Furthermore, node 2 and 3 benefit from excess energy originating from the PV generation of node 1 (cf. (d-e) on Fig. \ref{fig:scheduling}). However, beyond benefiting indirectly from the underlying decrease of the grid costs, node 1 also gets excess energy from nodes 2 and 3 respectively in the morning and evening. Note that no energy is stored at night as a significant amount of energy must be supplied and transit from the upstream grid. An additional storage load would yield a considerable increase of the associated bill.

Furthermore, from Fig. \ref{fig:scheduling}(f), the distinction between physically and virtually stored energy can be highlighted. The difference between both values correspond to either the hosted energy $e_{n,\mathrm{host}}^t$ by an individual if there is excess of physical storage space or the remote energy of an individual $e_{n,\mathrm{mut}}^t$ otherwise.

\subsection{Effects of different cost distributions}\label{sec:4c}
After the minimization of the total costs \eqref{eq:optim}, it is necessary to fairly and optimally distribute these costs to all members of the community. Both cost distribution keys (presented in Section \ref{sub:cost_distribution}) are compared, and outcomes are illustrated in Fig. \ref{fig:cost_distribution} for the final electricity bill of the $N$ = 3 nodes of the network. For the sake of comparison, results from the CO and PAR optimizations are also depicted.

\begin{figure}[!h]
\centering
\includegraphics[scale=1]{Figure5.eps}
\caption{Comparison of the final electricity bills of end-users with the different cost distribution keys.}
\label{fig:cost_distribution}
\end{figure}

We observe that the gains arising from the PAR optimization leads to costs reduction for all three nodes of the community with respect to the sole minimization of commodity costs. All consumers have thus a financial incentive for incorporating grid fees into their day-ahead scheduling. However, these gains are much lower for node 1, which can be explained by the fact that both CO and PAR optimizations result in a similar planning solution (they schedule most of the flexible load when the PV injection is high).
Overall, although improving the way end-users allocate their own resources can be profitable, these are incentivized into forming local communities to further reduce their electricity bill.

When global optimization is considered, the two cost distributions yield different trends. Under the present scenario, the resulting gains under the Nash equilibrium solution \eqref{eq:billing} generate smaller costs differences between community members than the outcome obtained with the Shapley value. Indeed, the latter option tends to reward actors who contribute most to the decrease of the commodity whereas the Nash equilibrium solution values the potential flexibility. In that regard, the significant contribution of node 1 highlighted in Section \ref{sec:4b} is better valued with the Shapley-based payoffs. The two options thereby give different incentives to fully leverage the flexibility of LV prosumers.
\begin{table}[h]
\centering
\caption{Impact of storage on costs}
\label{tab:storage}
\begin{tabular}{|c|cccc|}
\hline
Energy cost {[\euro{}]} & Node 1 & Node 2 & Node 3 & Total                   \\ \hline
ESS / Nash            & 24.25  & 35.97  & 47.42  & \multirow{2}{*}{107.64} \\
ESS / Shapley         & 19.75  & 36.39  & 51.50  &                         \\ \hline
No ESS / Nash              & 26.7   & 33.70  & 49.07  & \multirow{2}{*}{109.47} \\
No ESS / Shapley           & 21.38  & 36.49  & 51.60  &                         \\ \hline
\end{tabular}
\end{table}

These observations can be further highlighted by modifying the available storage capacity. Table \ref{tab:storage} gives the impact of storage on the energy cost for each node. From this table, we observe that if there is no available storage for nodes 1 and 3, the total electricity cost of the community is increased. In particular, the solution given by the Nash equilibium raises the electricity bill of both clients (1 and 3), while the Shapley-based outcome only affects node 1. Indeed, node 1 has less load flexibility than other members, and is thereby more impacted by the Shapley methodology that rewards the actual mobilized flexibility. It can be also noted that the absolute amount of the bill with zero ESS capacity could be much greater during a day with higher PV production. This results from the increased grids costs related to the higher injection.

\subsection{Benefits of sharing the grid fees at the community level}
\label{sub:comparison}
In this section, the outcomes obtained with our proposed cooperative approach (which properly considers non-linear grid costs) is compared with a benchmark representative of the current reality in most places worldwide. Hence, the latter design assumes an individual approach where each end-user optimizes its own cost function, in which grid costs are linearly integrated (proportional to the energy costs).

Table IV shows, for the same initial benchmark conditions, the relative differences of billings for various fixed grid rates (price per unit of consumed energy) in comparison to our cooperative approach with aggregative non-linear grid costs (a positive value corresponds to an increase of the costs).

\begin{table}[h]
\centering
\caption{Costs difference between aggregative and linear grid fees.}
\begin{tabular}{|c|ccc|}
\hline
\% costs difference & Node 1 & Node 2 & Node 3 \\ \hline
0.208 \euro{}/kWh      & 14.3   & 6.5    & 5.1    \\
0.30 \euro{}/kWh        & 48.5   & 37.2   & 35.2   \\
0.10 \euro{}/kWh        & -25.8  & -29.5  & -30.2  \\ \hline
\end{tabular}
\label{tab:difference}
\end{table}

Firstly, we can observe that even the optimistic case of a fixed grid price corresponding to the mean price obtained under the global optimization (0.208 \euro{}/kWh) leads to an increase of the billing for the three considered nodes. This comes from the fact that the individual optimization leads to higher imports (no sharing of surpluses). In reality, as there is no optimization across grid costs, the incurred costs should be even greater (c.f. individual approaches on Fig. \ref{fig:cost_approaches}) and a higher fixed rate could be expected. In that regard, the results show that increasing the fixed grid price (0.30 \euro{}/kWh) has a greater impact on node 1. This arises from its lower flexibility potential that prevents it from adapting its schedule. On the other hand, lower grid fees, i.e. 0.10 \euro{}/kWh (which could reflect a more efficient planning and operation of the whole system), is smoothing the differences among nodes.

So far, the results of an aggregative non-linear grid costs framework have been exposed considering both the individual and community approaches (c.f. Sections \ref{sec:4a} to \ref{sec:4c}), while this section introduced a linear grid costs framework under the individual approach. It should be noted that a community approach using linear grid costs could have been considered, but it is not straightforward and implies structural changes.

Indeed, the aggregative grid costs framework formalizes the interdependence of individuals sharing a same asset: the grid infrastructure. This naturally promotes cooperation since all the individual problems are linked to form a global problem. In this way, the mutualizing mechanisms are driven by the optimization of the global problem. On the contrary, linear grid costs leave the individual problems separable. Introducing mutualizing mechanisms in such framework is not driven by a natural consensus. On one hand, the PV excesses, although they can be possibly shared if the actors are not penalized (e.g. no injection grid costs if surplus are shared), find no natural consensus on a distribution key. On the other hand, an individual finds no interest in sharing its surplus of storage space unless it gets a financial advantage. Another market model should therefore be developed in such case. This further highlights the benefits of our approach reflecting the truth costs through the proper consideration of the aggregative nature of grid fees and the zero-marginal cost of sharing energy surpluses.

\section{Conclusion}
\label{sub:Conclusion}
This work has presented a new practical framework to optimally leverage the flexible resources distributed throughout low voltage networks. The solution aims at alleviating issues from centralized and fully distributed paradigms by relying on local communities (using the existing infrastructure). The paper firstly introduces a global optimization tool aiming at achieving the cost-optimal allocation of available resources at the community level, accounting for both commodity and grid-related costs. Then, the total gains are distributed among end-users using two different techniques, namely a Nash equilibrium and the Shapley value.

Results highlight the significant cost savings of forming a community with respect to the individual optimization of assets. Then, we observe that distributing the resulting costs using the Shapley value allows to endogenously reward the actors that contribute most to the costs reduction through their mobilized flexibility, whereas the Nash equilibrium tends to reward the potential flexibility consent. The two implementations thus offer different incentives to fully leverage the flexibility of the LV prosumers.

redpajama_set_name: RedPajamaArXiv


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Georges-André Klein est un artiste peintre orientaliste né le  à Paris, membre de la Société nationale des beaux-arts, mort le  à Ivry-sur-Seine.

Biographie
Après avoir suivi les cours de l'Académie Julian en 1918, de l'Atelier Biloul (où Il fait en 1920 la connaissance d'Eugène Dabit) et de l'École nationale supérieure des arts décoratifs où il se lie d'amitié avec les artistes qui formeront le groupe des peintres de la réalité poétique, Georges-André Klein, remarqué par Antoine Bourdelle, est appelé à travailler pendant sept années (de 1923 à 1929) avec le sculpteur dont il dessinera les maquettes de monuments et patinera les bronzes. Le dictionnaire Bénézit nous dit que la peinture de Georges-André Klein fut très tôt influencée par celle de , ce que Lynne Thornton nuance en estimant que Klein ne rencontra en réalité jamais Loutreuil, mais qu'il en approcha l'œuvre de façon très approfondie grâce à un ami commun rencontré en 1923, le peintre Christian Caillard.

Il n'est cependant pas déraisonnable de penser que Klein a bien fréquenté Loutreuil entre 1923 et la mort de ce dernier, dans sa quarantième année, en . Quatre complices, Eugène Dabit, Béatrice Appia, Christian Caillard et Georges-Henri Klein semblent avoir eu alors en commun d'admirer et de visiter amicalement le maître au n°20 de la Rue du Pré-Saint-Gervais, se constituant même, en hommage à leur aîné, en informelle École du Pré-Saint-Gervais<ref>[http://www.des-gens.net/Eugene-Dabit Site "La ville des gens", Les infos du Grand Paname, les écrivains de Belleville: Eugène Dabit, l'École du Pré-Saint-Gervais]</ref>. Eugène Dabit codifie ces souvenirs dans une nouvelle romancée, Un bal à Belleville, y évoquant, au-delà de l'atelier de Loutreuil, la fréquentation assidue par nos quatre artistes d'un bistrot célèbre de Belleville, le bar du Télégraphe.

C'est à la suite de sa visite émerveillée de l'Exposition coloniale internationale de 1931 que Georges-André Klein se rend au Maroc où il reviendra à chacun des hivers suivants. En 1936, il part pour une année entière à Madagascar , et d'où il visite les îles de La Réunion et Maurice. La Bourse de la ville de Paris qui lui est attribuée en 1937 est dotée d'un voyage, lui valant de repartir en 1938 pour un périple qu'abrège la Seconde Guerre mondiale. Notre artiste revient cependant en Algérie entre 1942 et 1945.

Après plusieurs séjours en Corse autour de 1950, notamment à Pino, après aussi des visites de l'Espagne et de la Sicile qu'il effectue pour une part avec son ancien ami Christian Caillard, Georges-André Klein se rend en 1958 pour la seconde fois à Madagascar, , rencontrant dans cette ville Victoire qu'il épouse en 1966, à Paris. En 1968, il passe cinq mois à Bamako.

 dira Jean-Pierre Delarge. En constituant, un an après la mort de Georges-André Klein survenue en 1992, le catalogue de sa succession, Dominique Ribeyre et Florence Berton établissent que les périples du peintre firent de lui également, à l'instar de son ami Pierre Bourut, un collectionneur éclairé.

 Contributions bibliophiliques
 Pierre Benoit, Œuvres complètes, tome IV, illustrations de Georges-André Klein (pour Les environs d'Aden avec une préface de Marcel Pagnol), Georges Pacouil, Victor Jean Desmeures, Paul Charlemagne, Roland Oudot, Claude Schürr, Jean-Pierre Alaux, Jean-Denis Malclès, Albin Michel, 1968.

 Expositions
 Expositions personnelles
 Galerie Bernier, 15, avenue de Messine, Paris, ,
 Galerie Marie L. André, Paris, mars-, .
 Dominique Ribeyre et Florence Baron, vente de l'atelier et de la collection Georges-André Klein, Hôtel Drouot, .

 Exposition collectives
 Salon des indépendants, Paris, à partir de la décennie 1920.
 Madagascar vu par nos peintres et nos sculpteurs, Musée de la France d'Outre-Mer, Paris, 1946.
 Salon d'automne, Paris, 1947, 1950.
 Salon des Tuileries, Paris, juin 1948, 1950.
 Premier Salon Biarritz - San Sebastian - École de Paris, peinture, sculpture : Yvette Alde, André Beauce, Georges-André Klein, Adrienne Jouclard, Jehan Berjonneau, Louis Berthomme Saint-André, Roland Bierge, Maurice Boitel, Andrée Bordeaux-Le Pecq, Rodolphe Caillaux, Jack Chambrin, Jean Cluseau-Lanauve, Jean-Joseph Crotti, Gen Paul, Antonio Guansé, Henri Hayden, Franck Innocent, Daniel du Janerand, Jean Joyet, Germaine Lacaze, André La Vernède, Robert Lotiron, Roland Oudot, Maurice Verdier, Henry de Waroquier…, Casino Bellevue, Biarritz et Musée San Telmo, Saint-Sébastien (Espagne), juillet-.
 Des natures mortes à Honfleur, Galerie Danielle Bourdette-Gorzkowski, Honfleur,  - .
 Regards croisés, Galerie Danielle Bourdette-Gorzkowski, Honfleur, .

 Réception critique
  - Michel Florisoone
  - Connaissance des arts
  - Marion Vidal-Bué

 Prix et distinctions

 Collections publiques

 Collections privées
 Pierre Bourut, Portraits de Pierre Bourut, huiles sur toiles.
 Robert Martin, La maison de Christian Caillard à Jávea, huile sur toile.
 Tony Curtis, Henderson (Nevada), Bouquet de roses au vase bleu.

 Références

 Annexes
 Bibliographie
 Eugène Dabit, Un bal à Belleville, nouvelle, in Ville Lumière, Éditions Le Dilettante, 1937.
 Roger Bezombes, L'exotisme dans l'art et la pensée, Éditions Elsevier, 1953.
 « Georges-André Klein, exotisme discret », Connaissance des arts, n°45, .
 Georges-André Klein, Éditions Galerie Marie L. André, 1965.
 Raymond Charmet, Georges-André Klein, Éditions Galerie Marie L. André, 1970.
 Lynne Thornton, Les africanistes, peintres voyageurs, ACR Édition, 1990.
 Patrick-F. Barrer, L'histoire de Salon d'automne de 1903 à nos jours, Éditions Arts et Images du Monde, 1992.
 Dominique Ribeyre et Florence Baron, Catalogue de la vente de la succession Georges-André Klein - tableaux et collection de l'artiste, notamment art islamique, Hôtel Drouot, Paris, .
 André Roussard, Dictionnaire des artistes à Montmartre, Éditions André Roussard, 1999.
 Emmanuel Bénézit, Dictionnaire des peintres, sculpteurs, dessinateurs et graveurs, Gründ, 1999.
 Marion Vidal-Bué, L'Algérie et ses peintres, Éditions Paris-Méditerranée, 2000.
 Jean-Pierre Delarge, Dictionnaire des arts plastiques modernes et contemporains, Gründ, 2001.
 Adrian Darmon, Autour de l'art juif - Encyclopédie des peintres, photographes et sculpteurs, Éditions Carnot, 2003, .
 Pierre Sanchez (préfaces de Josiane Sartre et Chantal Beauvalot), Dictionnaire du Salon des Tuileries (1923-1962) - Répertoire des exposants et liste des œuvres présentées'', L'Échelle de Jacob, Dijon, 2007.

Liens externes

Naissance en décembre 1901
Naissance dans le 4e arrondissement de Paris
Peintre français du XXe siècle
Peintre figuratif français
Peintre africaniste
Peintre paysagiste français
Peintre français de nature morte
Peintre portraitiste français
Élève de l'Académie Julian
Chevalier de la Légion d'honneur
Décès en octobre 1992
Décès à Ivry-sur-Seine
Décès à 90 ans

redpajama_set_name: RedPajamaWikipedia


text:
Jodie Foster & Mike Bloomberg collaborate on video "Vote. Because It Matters."
ART SHRIAN November 05, 2018 #BecauseItMatters, VOTE, Vote. Because It Matters.
"Vote. Because It Matters."
Stars Urge Women to Vote in Midterm Elections in New Ad Produced by Mike Bloomberg and RadicalMedia, and Directed by Jodie Foster
View the VOTE #BecauseItMatters ad here
New York, NY — In a new ad released this morning produced by Mike Bloomberg and RadicalMedia, and directed by Jodie Foster, stage, screen, television, and social media stars, and women from across the nation urge other women to vote in the midterm elections on November 6th "Because It Matters." This is the latest ad in the largest digital effort supporting Democrats for the House and will run nationally and in competitive house races through Election Day.
"It is hard to overstate the importance of this election. Our environment and our health are on the line," said Mike Bloomberg. "The good news is that more women are running than ever before, and female voters overwhelmingly support Democratic candidates for the House and Senate. The polls suggest a gender gap in voting larger than anytime since the 1950s. But this election will be decided by turnout and getting people to cast their ballots. I want to thank Jodie Foster and every woman who participated in this effort for making their voices heard and encouraging others to do the same."
The ad, which is funded by Independence USA PAC, features appearances by Ser Anzoategui, Tichina Arnold, Hannah Bronfman, Logan Browning, Sophia Bush, Cher, Laverne Cox, Minnie Driver, Jodie Foster, Bethenny Frankel, Isabella Gomez, Marilu Henner, Felicity Huffman, Jasmine Cephas Jones, Gloria Calderon Kellett, Minka Kelly, Zosia Mamet, Christine Lahti, Téa Leoni, Marlee Matlin, Julianne Moore, Olivia Munn, Kathy Najimy, Jaina Lee Ortiz, Piper Perabo, Ellen Pompeo, Lele Pons, Lily Tomlin, Christy Turlington-Burns, Constance Wu, and more.
The women ask viewers if they care about issues such as immigration, healthcare, climate change, women's rights, LGBTQ rights, basic human rights, gun safety and gun reform, and tell them if so, to not lose hope but to "Vote. Because It Matters."
"Women's voices are being listened to in a way that they haven't been before. And it's not just women candidates. It's women voters and women activists," said director Jodie Foster. "I'm proud to partner with RadicalMedia and Mike Bloomberg on creating a campaign that encourages all Americans to use their voice and vote. Women across the country have concerns and strong points of view and they can make a difference by going to the polls on November 6th. We hope that this campaign, featuring familiar faces in the entertainment industry, will inspire others to share their views and more importantly take action on Election Day. It really matters."
"RadicalMedia is proud to be part of this important get out the vote campaign," said Jon Kamen, Founder & CEO of RadicalMedia. "Jodie Foster's direction and passion energized everyone on set and inspired a diverse group of women in the entertainment industry to participate in the project. We applaud Mike Bloomberg's commitment to this effort enabling voices to be heard… because it matters."
About Independence USA PAC:
Independence USA PAC is a Mike Bloomberg-funded effort to support candidates and referenda in local, state and federal races across the country, with a focus on issues including gun laws, the environment and education policy. To learn more about Independence USA PAC, visit http://www.independenceusapac.org/.
About RadicalMedia:RadicalMedia is an Oscar-, Emmy-, Peabody- and Grammy Award-winning studio, with recent credits that include "Bobby Kennedy for President" and "My Next Guest Needs No Introduction with David Letterman" for Netflix; "The Fourth Estate" for Showtime; "MARS" and the Emmy-nominated, "Year Million" for National Geographic; "Stan Against Evil" for IFC; "Hamilton's America" for PBS' Great Performances; Netflix's "Abstract: The Art of Design,"; and "May It Last: A Portrait of the Avett Brothers," which won the Audience Award: 24 Beats Per Second at SXSW 2017 and was acquired by HBO. RadicalMedia's vast body of work also includes the Oscar-winning documentary "The Fog of War"; Oscar-nominated and Emmy-winning "What Happened, Miss Simone?" for Netflix; "Keith Richards: Under the Influence" for Netflix; and Epix's docuseries "America Divided;" as well as numerous Joe Berlinger directed projects, including the Oscar-and Emmy-nominated "Paradise Lost: Purgatory" for HBO; "Metallica: Some Kind of Monster"; "Under African Skies" for A&E; "Whitey: The US vs. James J. Bulger" for CNN and the 4-part docuseries "Killing Richard Glossip," debuting this month on Investigation Discovery. See more at RadicalMedia.com and find us on Facebook, Twitter, and Instagram.
Labels: #BecauseItMatters, VOTE, Vote. Because It Matters.

redpajama_set_name: RedPajamaCommonCrawl


The story of Mowgli – the boy who was raised by a pack of wolves – is well-known and the recent Disney film on it is raking in millions all over. The fact that a young child could be raised by animals and live among them is what has fascinated us about this enchanting tale.
However, while Mowgli's tale was all fiction – conjured up by Rudyard Kipling – you would be surprised to know there have been countless Mowgli-like cases in the real world as well; that of feral children. A feral child is someone who has stayed away from human contact and has been brought up among animals. The list below tells the story of 10 such real-life feral children which will leave you stunned.
Possibly one of the most famous cases of feral children ever recorded, Kamala, 8, and Amala, 12, were discovered in a cave by a Reverend in 1920. The Reverend had been noticing the two physically deformed children for some time and had seen them running on all fours. The man took the two children home where they would only eat raw meat and tear off their clothing. Both, however, had an acute sense of hearing and sense of smell. Unfortunately, Amala died in 1921 and Kamala survived for 9 more years before succumbing to kidney failure.
Found as a young boy merrily playing with a bunch of wolves in the forest of Musafirkhana (near Sultanpur, India) in 1972, Shamdeo shocked everyone who met him. He had long fingernails, tousled hair and calluses all over his body. He thirsted for blood, could hunt chickens easily, loved darkness and appeared very friendly with dogs and jackals. After being taken in by some social welfare organizations, Shamdeo died in February 1985.
The story of Oxana Malaya from Ukraine was quite tragic as she was left outside by her alcoholic parents when she was just three. Seeking some warmth, little Oxana went inside a dog kennel. Astonishingly, the dogs raised her lovingly and she lived with them for six long years. Oxana was eventually found in 1991 outside that kennel, playing with the dogs. By this time, she had imbibed several traits of a canine: running on all fours, panting with the tongue out and barking. It was only after intensive therapy that Oxana could learn human and social skills again.
Sujit's is another rather distressing story. As a young child in early 1970s, Sujit would at times show abnormal behaviour and his parents would then lock him up in a chicken coop at their farm in Fiji. After both his parents died, Sujit's grandparents decided to lock the poor boy in the coop for good. Fortunately, he was found in 1978. By this time, Sujit would make clicking sounds, peck at his food and crouch on a chair. Later, he was discovered by a kind woman who nurtured him and is still tending to him. Sujit is now on the recovery path.
After being maltreated by his family for years, 4-year-old Ivan Mishukov of Russia decided to run away from home into the forests. There, he met a pack of dogs and stayed with them. For two years, Ivan stayed with the dogs and even became the leader of their pack; sharing food with them from begging, supervising them and taking care of everyone. Eventually, Ivan was caught in 1998 and was taken to a children's home where he recovered quickly.
She is one of those rare feral children who could actually speak something coherent when she was found. Memmie Le Blanc traversed through the forests of France for a decade and her diet primarily consisted of birds, frogs, branches and leaves. She could even skin and devour little animals with ease and swing from tree to tree like a monkey. She had extraordinary eyesight and was a very fast runner. She was eventually found by a rich patron who tended to her and ensured that the girl became completely normal. Memmie went on to become a nun and died at the age of 63 in France.
Also famously called as 'The Monkey Boy', John Ssebunya of Uganda had fled to the forests when he saw his father murder his mother one night. John began living with the moneys in the forests and pretty soon acquired many of their traits like eating roots and berries and climbing up trees. When he was discovered in 1991, John was six and had several afflictions. He underwent treatment and made a full recovery soon. 'The Monkey Boy' now leads his life as a singer.
In a very peculiar incident which happened in 1912 in the North Cachar Hills near Assam, India, a young boy was stolen from his parents by a leopardess. Curiously, though, the leopardess did not kill the boy and instead raised him for three years. When he was finally found out in 1915, he could run rapidly on all fours and could eat small birds easily. He had calluses all over his body and his palms and toes were covered with very tough horny skin. 'The Leopard Boy' later, under rigorous therapy, learnt to speak and walk upright.
When he was rescued by Russian health care workers, seven-year-old Prava could only communicate by chirping like a bird. The little boy had been kept in a two-bedroom apartment for years, which also worked as an aviary, by his mother. For some odd reasons, the mother considered Prava as one of her pets and never even spoke to him. Hence, Prava could only speak bird language. Thankfully, he was rescued and then rehabilitated in 2008 and is now recovering steadily.
The most heartbreaking story in this list, little Marina was first kidnapped at the age of five and then left in the jungles of Colombia by her abductors in the 1950s. There, Marina lived among a troop of capuchin monkeys who took care of her fondly; even rescuing her from poisoning once. Unfortunately, when she was found by some hunters a few years later, she had lost her ability to speak and was sold to a brothel. Marina somehow managed to escape from there but was then enslaved by a mafia family. Finally, she was saved by a neighbour and eventually hired as a housekeeper in the UK. Marina now leads a happily married life there and has also written a book about her experiences.


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One of the best ice skating rinks in Mississauga, ON, Woodhurst Heights Park Ice Skating Rink is a 1 sheet outdoor ice skating rink is open year round.
Ice skating sessions for All Ages are one of the main attractions at Woodhurst Heights Park. Ice Skating provides great exercise and an opportunity to get out of the house – plus, it is not like exercising at the gym… skating is fun! Lace-em up and come join the others. Get on the ice and get ready for a great experience.
If you do not see the rinks public ice skating schedule posted, be sure to contact them at (905) 615-4770 for their public session times.
Woodhurst Heights Park Ice Skating Rink offers pickup ice hockey for youths.Give Woodhurst Heights Park a call at (905) 615-4770 to inquire about their pickup hockey schedule if it is not listed in the description or schedule here.


Red Mountain Tire provides Parking Brake Adjustment services to Mesa, AZ, Apache Junction, AZ, Gilbert, AZ, and other surrounding areas.
Why Should You Have Parking Brake Adjustment Services Performed at Red Mountain Tire?
We proudly service the Parking Brake Adjustment needs of customers in Mesa, AZ, Apache Junction, AZ, Gilbert, AZ, and surrounding areas.


text:
Andy Kulberg
Classically trained at New York University, the late flautist/bassist Andy Kulberg anchored one of rock's most influential ensembles; Blues Project. Composer of "Flute Thing" Andy was among the first wave of bassists who drew from jazz, blues, and folk in an improvisational rock context.
Following Blues Project, Andy formed Seatrain, which broke ground in rock roots music including a fine self-titled sophomore slab produced by George Martin.
Ian Dury / Hit Me With Your Rhythm Stick
Dexys Midnight Runners / Searching for the Soul Rebels


text:
Q: addTarget doesn't work for UIButtons in iOS, view covered up I have two UIButtons I am creating programmatically and setting targets. If I add these buttons to a main view, everything works beautifully. However when I add the to a subview first and add this subview to the main view, touch events don't work. I'm guessing these buttons are being covered up.
How can I uncover these buttons while keeping them inside the subview?
Here is my code:
// Create button panel here
UIImage *buttonPanel = [UIImage imageNamed:@"left_button_background"];
UIImageView *buttonPanelView = [[UIImageView alloc] initWithImage:buttonPanel];
[buttonPanelView setFrame:CGRectMake(20, 186, 363, 345)];

// Populate the panel with buttons
UIButton *cmsButton = [[UIButton alloc] initWithFrame:CGRectMake(10, 10, 351, 142)];
[cmsButton setImage:[UIImage imageNamed:@"BTN_MATLIB"] forState:UIControlStateNormal];
[cmsButton addTarget:self action:@selector(loadCMS) forControlEvents:UIControlEventTouchDown];
[buttonPanelView addSubview:cmsButton];
[self setCms:cmsButton];

UIButton *calcButton = [[UIButton alloc] initWithFrame:CGRectMake(10, 196, 351, 142)];
[calcButton setImage:[UIImage imageNamed:@"BTN_MORE_RESOURCES"] forState:UIControlStateNormal];
[calcButton addTarget:self action:@selector(loadCalc) forControlEvents:UIControlEventTouchDown];
[buttonPanelView addSubview:calcButton];
[self setCalc:calc];

[[self view] addSubview:buttonPanelView];

A: Image views do not have user interactions enabled by default, which means none of their subviews can receive user interactions either.
buttonPanelView.userInteractionEnabled = YES;

redpajama_set_name: RedPajamaStackExchange


text:
Chris Woods : The Way of the Cross
Penrice, Father James and Woods, Chris and Wallace, Rory. Chris Woods : The Way of the Cross. Vancouver, BC: Diane Farris Gallery, 1995.
While Woods explains his working methods, Wallace examines how the artist responded to the challenge of producing a modern version of the "Stations of the Cross" commissioned for an Anglican church in Vancouver. Father Penrice comments on the history and relevance of the "genre". Biographical notes. 18 bibl. ref.
Penrice, Father James (Author); Woods, Chris (Artist); Woods, Chris (Author); Wallace, Rory (Author); Farris, Diane (Prefacer)
410 - WOODS, CHRIS (1970)
[70] p. : 49 ill. (14 col.) ; 22 x 18 cm
Vancouver, BC: Diane Farris Gallery
Woods, Chris
Exhibition dates: 11 Jan. - 10 Feb. 1996, Diane Farris Gallery (Vancouver).


October is another major month for tourism in Egypt. Its a very popular time to visit the country for two reasons. The first is the great weather Egypt experiences during the beginning of the cool month. Temperatures in October are in the high 70sF/low 80sF (mid 20sC) in most of the country, with Upper Egypt cooling off to temperatures in the 90F (35C). The second and perhaps more interesting reason is the Abu Simbel Sun Festival that takes place on October 22nd. On this date, traditionally believed to be the date of Ramses IIs coronation, the sun aligns with specific openings in the temple, illuminating statues of Ramses II and the sun gods, leaving the statue of the god Ptah, god of darkness, in the dark all year long. Its a very good time of year for this festival to take place, since Abu Simbel is pretty far south, in an area that can get pretty warm during the summer months.


Janet George has been practicing family law for over 35 years and is widely recognized as one of the top family law attorneys in the state of Washington. She limits her practice to complex, high asset and high income cases, including those involving property characterization, business valuations, and the distribution of multi-million dollar estates. She has represented high net worth individuals across different fields, including business owners, corporate executives, legal and medical professionals, and professional athletes.
Janet has received the top honors of her field. She has been a Fellow of the American Academy of Matrimonial Lawyers (AAML) since 1992, serving as President of the Washington AAML chapter from 1997 to 1999. She has also been included in Best Lawyers in America for the past five years, Super Lawyers since 2003, and has had a peer-review rating of "AV Preeminent" by Martindale Hubbell for the past 30 years.
Before becoming an attorney, Janet earned a Master's degree in psychiatric nursing, counseling families in crisis and working with adolescents at Seattle Mental Health Institute as Director of Nursing and also as a Psychiatric Nurse. She considers this experience a natural background for the practice of family law.
Janet continues to take cases that involve parenting disputes as part of her ongoing passion to help children. She is also a strong supporter of organizations that share this mission, including King County CASA and Treehouse, a non-profit that advocates for foster children.
When time allows, Janet is also an adjunct professor at Seattle University School of Law and considers working with law students one of her greatest joys.
Following her own advice to live life completely, Janet is a former small plane pilot – flying to and from her getaway in Sun Valley in her 182 RGTurbo Cessna. She has dealt blackjack at South Shore Tahoe, and has shown quarter horses in the Salinas rodeo. She's an avid skier and 'wannabe' golfer, and is currently involved in the world of horse racing. She owns a percentage in four race horses and enjoys spending time at Emerald Downs with the jockeys, trainers, and other owners and breeders.
Longtime supporter of King County Family Law CASA and Treehouse, a non-profit that advocates for foster children.
Regular speaker and chairperson at family law and other area CLE presentations; most recently "Mastering Social Media" (KCBA, 2015) and "Family Law Hot Topics" (KCBA, 2014).
Washington Family Law Deskbook, "Methods of Discovery in Family Law Litigation," 1999 and updated in 2012.


text:
Anaxilaos nebo Anaxilas () byl králem Sparty (pravděpodobně mytickým) přibližně od roku 645 před Kr. Do roku 625 před Kr. Pocházel z královského rodu Eurypontovců.

Nejstarší známý záznam od historika Herodota v knize Historie, Anaxilaa uvádí jako jedenáctého krále Sparty rodu Eurypontovcov od jejího legendárního zakladatele Prokom.
Z tohoto textu se také dozvídáme, že jeho otcem a předchůdcem na trůnu byl Archidamos I. a následníkem syn Leótychidas I. Jiné informace týkající se krále Anaxilaa nám Herodotos nepodává.

To, zda byl Anaxilaos skutečně panovníkem Sparty nevíme, neboť je znám i seznam králů Sparty rodu Eurypontovců od Pausania, který se s Herodotovy celkem neshoduje a král Anaxilaos v něm nefiguruje.

Jak se antičtí historici v seznamech králů rodu Eurypontovců (v seznamu rodu Agiovců se shodují) neshodli, tak i současní nejsou na tom odlišně. Chybějící historický materiál z tohoto období dějin králů Sparty, pro následné kusé rukopisné záznamy antických autorů napsáno až po delším časovém odstupu a navíc plné rozporů, nám asi neumožní poodhalit historii této dávné minulosti Sparty.

Reference

Literatura
 Herodotos, Historie, VIII, 131.
 Pausanias, Periégésis TES Hellados, 3,7,5–7;
 Jona Lendering, Eurypontids and Agiads,
 Paul Cartledge, Sparta and Lakonia: a regional history, 1300-362 BC,

Spartští králové
Muži


The conclusion of special counsel Robert Mueller's investigation into Russian interference in the 2016 election would in normal circumstances have provided plenty of comic fodder for late night hosts to scrutinize.
However, as news of its wrapping up came Friday, the comedians who weren't on air that night didn't have much chance to offer their humorous take on the development ― so some scrambled on Twitter to have their say.
"Full Frontal with Samantha Bee" spoofed the report, which has been submitted to Attorney General William Barr.
The Mueller report could be very damning if it contains any of the things we've seen the President do and say in public.
I know a lot of you have been asking for an emergency pod about the Mueller Report but we're gonna try something crazy and wait until we know what's in the Mueller Report.
Since Mueller's appointment in May 2017, Trump has tweeted the term "witch hunt" 178 times—an average of about once every four days.
We will update this story with more late night reaction as it comes in.


text:
Personal (Personal) è un romanzo del 2014 di Lee Child, il diciannovesimo della serie che ha come protagonista Jack Reacher.

Nel 2014 il libro ha vinto il Premio RBA de Novela Policiaca.

Trama
Jack Reacher è un ex maggiore della polizia militare dell'esercito USA. Mentre si sta godendo il viaggio senza fine, senza una casa, senza ordini a cui obbedire... che ha scelto come modo di vivere, nota un annuncio su un giornale dell'esercito lasciato su una panchina. Qualcuno a cui lui deve un favore lo sta richiamando in azione, non può non rispondere. Reacher deve tornare in azione per trovare un suo vecchio nemico, arrestato in passato ed uscito di prigione dopo aver scontato la pena di 15 anni. Purtroppo si tratta di uno dei migliori cecchini al mondo e pare che sia stato proprio lui a sparare al Presidente della Repubblica francese da una distanza impossibile… solo poche persone al mondo possono colpire una persona a più di 1300 metri!

Note

Collegamenti esterni

Romanzi di Lee Child
Romanzi thriller


How do I register on Tinsley Island?
After you have docked, please register HERE. You can also use the on-Island registration stations located at the Lanai Bar and at the West Dock Bathhouse.
Does the island offer storage for galley items and perishables?
Yes. When cooking your meals on the Island, you may store your galley items in the lockers in the galley area instead of taking them back and forth to your boat. Members may padlock and place their boat or family name on a locker. Lockers are available on a first-come/first-served basis beginning March 1.
There are refrigerators and freezers in the galley area, and they fill up quickly. You will need a milk crate or a plastic container with your boat or family name for your perishables. If you have a refrigerator on your boat, please use that and leave the Island's facilities free for those who do not access to a personal refrigerator.
Is there a snack bar on the island or food available?
There is a Snack Bar on the Island, open on the weekends. The Snack Bar is closed during Cruises.
Can I do my laundry on the Island?
Yes. We have a laundry room located behind the galley area. There are five washers and five dryers. You will need quarters. The washers take about 35 minutes and dryers 45 minutes.
Are visitors allowed to go to the Lighthouse and climb the tower?
Yes, the Lighthouse has an observation post at the top that members are welcome to enjoy. However, keep in mind that people are staying in the Lighthouse, so be sure you do so quietly and during reasonable hours. Please take care ascending and descending the ladder.
Can Island visitor use the Lighthouse kitchen and bathrooms?
No. The kitchen and bathrooms in the Lighthouse are for the use of the Lighthouse occupants only.
What activities are available for visitors on the Island?
Aside from relaxing by the pool and swimming, you might enjoy our regulation bocce ball courts, fitness center, horseshoes and volleyball courts. We also keep Lasers, kayaks, paddleboards and paddleboats at the West Dock Shed. Paddles are signed out at the West Dock. Please remember: there aren't enough for everyone, so watch your time and return them when you've finished.